Question

Three consecutive even integers have a sum of 54.

Answer 1

To find three consecutive even integers that sum to 54, represent the first integer as x, and the others as x+2 and x+4. Solve the equation x + (x + 2) + (x + 4) = 54 to find x = 16, and thus the integers are 16, 18, and 20.

Step-by-step explanation:

Consecutive Even Integers with a Sum of 54

To solve the problem involving consecutive even integers with a sum of 54, we first need to define the integers. Let's represent the first even integer as x.

Because we're dealing with consecutive even integers, the second and third integers can be represented as x+2 and x+4 respectively. The sum of these integers is given by the equation:

1. x + (x + 2) + (x + 4) = 54
2. 3x + 6 = 54
3. 3x = 54 - 6
4. 3x = 48
5. x = 48 / 3
6. x = 16

Therefore, the first even integer is 16. The second and third consecutive even integers are 18 and 20, respectively. These three integers (16, 18, 20) add up to 54, thereby solving the problem.